/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int widthOfBinaryTree(TreeNode* root) {
        vector<pair<TreeNode*, unsigned int>> q;    // 用数组模拟队列
        q.push_back({root, 1});

        unsigned int ret = 0;
        while(q.size())
        {
            // 先更新这一层的宽度
            auto& [x1, y1] = q[0];
            auto& [x2, y2] = q.back();
            ret = max(ret, y2 - y1 + 1);

            // 让下一层进队
            vector<pair<TreeNode*, unsigned int>> tmp;  // 让下一层进入这个队列
            for(auto& [x, y] : q)
            {
                if(x->left)
                    tmp.push_back({x->left, y * 2});
                if(x->right)
                    tmp.push_back({x->right, y * 2 + 1});
            }
            q = tmp;
        }
        return ret;
    }
};